I think you have to take your cue from her and what she is telling you. You have no obligation to go to the birthday party.

You say you are sorry, but you minimize the offense by saying it was just "a few bad comments/jokes . . . " There's the problem right there. You don't think what you said was any big deal. Denigrating the appearance of a girl or woman is a pretty sure-fire way to torpedo a romance. You don't seem to get it. That's what she thinks.